Dynamics on networks of cluster states for globally coupled phase oscillators

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Dynamics on networks of cluster states for globally coupled phase oscillators

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Orosz, Gábor en_GB
dc.contributor.author Wordsworth, John en_GB
dc.contributor.author Townley, Stuart en_GB
dc.contributor.department University of Exeter en_GB
dc.date.accessioned 2009-01-16T16:31:43Z en_GB
dc.date.accessioned 2011-01-25T10:33:34Z en_US
dc.date.accessioned 2013-03-20T12:36:18Z
dc.date.issued 2007 en_GB
dc.description.abstract Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. We investigate such a heteroclinic network between partially synchronized states where the phases cluster into three groups. For the coupling considered there exist 30 different three-cluster states in the case of five oscillators. We study the structure of the heteroclinic network and demonstrate that it is possible to navigate around the network by applying small impulsive inputs to the oscillator phases. This paper shows that such navigation may be done reliably even in the presence of noise and frequency detuning, as long as the input amplitude dominates the noise strength and the detuning magnitude, and the time between the applied pulses is in a suitable range. Furthermore, we show that, by exploiting the heteroclinic dynamics, frequency detuning can be encoded as a spatiotemporal code. By changing a coupling parameter we can stabilize the three-cluster states and replace the heteroclinic network by a network of excitable three-cluster states. The resulting “excitable network” has the same structure as the heteroclinic network and navigation around the excitable network is also possible by applying large impulsive inputs. We also discuss features that have implications for related models of neural activity. en_GB
dc.identifier.citation 6 (4), pp. 728-758 en_GB
dc.identifier.doi 10.1137/070683969 en_GB
dc.identifier.uri http://hdl.handle.net/10036/47620 en_GB
dc.language.iso en en_GB
dc.publisher Society for Industrial and Applied Mathematics en_GB
dc.relation.url http://dx.doi.org/10.1137/070683969 en_GB
dc.subject globally coupled oscillators en_GB
dc.subject three-cluster state en_GB
dc.subject heteroclinic connection/network en_GB
dc.subject winnerless competition en_GB
dc.subject excitable dynamics en_GB
dc.subject neural computation en_GB
dc.title Dynamics on networks of cluster states for globally coupled phase oscillators en_GB
dc.type Article en_GB
dc.date.available 2009-01-16T16:31:43Z en_GB
dc.date.available 2011-01-25T10:33:34Z en_US
dc.date.available 2013-03-20T12:36:18Z
dc.identifier.issn 1536-0040 en_GB
dc.description Copyright © by Society for Industrial and Applied Mathematics. Unauthorized reproduction of this article is prohibited. Its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. en_GB
dc.identifier.journal SIAM Journal on Applied Dynamical Systems en_GB


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